I received this cube via email from Bogdan Golunski
of Germany on November 26, 2003. It is not associated, and must be classed
as a pantriagonal magic cube even though it contains many magic squares.
All 13 of the horizontal planes and all 13 of the planes parallel to the
front of the cube are pandiagonal magic squares. All broken diagonals and
12 of the 13 main diagonals in 1 direction of the vertical planes parallel
to the sides of the cube sum incorrectly. Because of this, only 1 of these
13 planes is a simple magic square. 3 of the 6 oblique planes are simple
magic squares and 3 are pandiagonal magic squares.
Total for the cube, 4 simple magic squares and 29 pandiagonal magic
squares.

All pantriagonals in this cube sum correctly. So, because all 3m
orthogonal planes in this cube are not magic squares (and the same type),
this cube must be classed only as pantriagonal magic! A most unusual cube!

This cube is not associated. It is perfect and so
contains 9m pandiagonal magic squares. That is 3 * 13 = 39
orthogonal order 13 pandiagonal magic squares, 6 oblique, and 6m-6
broken oblique order 13 pandiagonal magic squares.
The fact that there are 6m-6 broken oblique pandiagonal magic
squares in a perfect cube was first mentioned by Rosser and Walker in 1938
[1]. It was mentioned again in
Liao's paper [2].

This cube contains 507 1-agonals (rows,
columns and pillars) [3]
1014 pan-2-agonals (pan-diagonals)
676 pan-3-agonals (pan-triagonals)
The discrepancy between the above agonals (number lines) is due to the
fact that the same line of numbers appear in several different magic
squares.

This is one of the 6m-6 broken oblique planes
from the above cube. All are pandiagonal magic squares. this is the case
for all nasik perfect magic cubes! [1][2]

[1] B. Rosser and R. J. Walker, Magic
Squares: Published papers and Supplement, 1939, a bound volume at Cornell
University, catalogued as QA 165 R82+pt.1-4. All papers are very
technical. There are NO diagrams. The bound book contains:

On the Transformation Group for
Diabolic Magic Squares of Order Four, Reprinted from Bulletin of the
American Mathematical Society, June 1938.

A continuation of The Algebraic Theory
of Diabolic Magic Squares on typewritten pages numbered 729 – 753. (This
starts with a new section 6, renamed from ‘conclusion’ to ‘Latin
Squares’). Pages 736 to 753 is about diabolic (perfect) magic cubes and
points out there are 3m diabolic magic squares parallel to the faces of
the cubes and 6m diabolic magic squares parallel to six diagonal planes.

This is a simple magic cube and is not associated.
Only rows, columns pillars and the 4 main triagonals sum correctly to
19215.
This cube contains no magic squares. I received it from Abinhav Soni as an
email attachment on Nov. 29, 2003